I have a 16gb card which I have transferred a few videos and books onto, but after a few days on my Galaxy tab the files have disappeared. I have tried three different cards, using different types of files, but after a few days they are always gone. Any ideas?
Is this a SD card that you have used for a long time on other devices? Do you, or have you, done a lot of writing to it?
SD cards have a limited lifespan, so the less amount of writing you can do to it, the better. You might want to do a chkdsk on it to see if it finds any bad sectors. If you find any, that would be your culprit.
I've had SD cards last for about a year and then files start disappearing, etc. That's when I would use it for everything - as the main SD card (swapping it), which means a lot of writing as apps save their data, backing up nightly with Titanium Backup, saving photos, caching, etc.
Once I learned about the limited lifespan of SD cards, I finally retrained myself to not use it as the main SD card. Now, I do weekly backups, once a week and I only store my music on the SD card, and photos that I take with the camera. The latest SD card I have has now lasted over a year which is longer than the others before it.
Also, quality of SD cards is a given. Don't go for the cheaper, off-name brands. They don't last long. It's better to shell out a few extra bucks and get a name brand.
This happened to me both with my Samsung Galaxy S4 and with my Galaxy Note tablet several times. Samsung products in particular are very specific about which MicroSD cards they can work with. The general advice for this situation is to buy a Samsung brand memory card for the phone, as there should be less issues with it.
Before you try that, make sure to format your current card on your tablet. Formatting it on your PC will result in a slightly different memory format that may not be as compatible with your Tab. Here are instructions on how to format your card: http://eguides.sprint.com/support/eguides/samsunggalaxytab3/index.html#samsung_galaxy_tab_3_ug/format_a_memory_card.html
This will delete all data on the card, so make sure to back up your important files (if any still remain) before you format the card. Best of luck to you!